根据tan45°=tan(21°+24°)=tan21°+tan24° | 1-tan21°tan24° | =1 得到tan21°+tan24°=1-tan21°tan24°, 可得tan21°+tan24°+tan21°tan24°=1 同理得到tan22°+tan23°=1-tan22°tan23°, tan22°+tan23°+tan22°tan23°=1; (1+tan21°)(1+tan22°)(1+tan23°)(1+tan24°) =[(1+tan21°)(1+tan24°)][(1+tan22°)(1+tan23°)] =(1+tan24°+tan21°+tan24°tan21°)(1+tan22°+tan23°+tan22°tan23°) =(1+1-tan24°tan21°+tan24°tan21°)(1+1-tan22°tan23°+tan22°tan23°) =4 故选C. |